Question

For a series RLC circuit which of the following statement is not correct?

• A. \( \omega L>\frac{1}{\omega C} \), \( \phi \) is positive. In this case the voltage leads the current by an angle \( \phi \)
• B. \( \omega L<\frac{1}{\omega C} \), \( \phi \) is negative. In this case the current lags the voltage by an angle \( \phi \)
• C. \( \omega L = \frac{1}{\omega C} \), \( \phi = 0^\circ \). In this case the voltage and current are in phase
• D. The impedance is purely resistive and minimum when \( \phi = 0 \), Z=R

Hint:

\(\phi\) is positive for inductive circuits (V leads I).
\(\phi\) is negative for capacitive circuits (I leads V).
\(\phi = 0\) for resonant circuits (V and I in phase).
Awkward phrasing like "lagging by a negative angle" usually implies leading by the positive magnitude.

Answer 1

The Correct Option is B

In a series RLC circuit, the relationship between the inductive reactance (\(XL\)) and the capacitive reactance (\(XC\)) determines the phase angle (\(\phi\)) between the voltage and the current. The statements provided evaluate this relationship: 

• Option 1: \( \omega L>\frac{1}{\omega C} \) implies \(XL > XC\), resulting in a positive phase angle (\(\phi\)), where voltage leads current. This is correct.
• Option 2: \( \omega L<\frac{1}{\omega C} \) suggests \(XL < XC\), typically causing a negative phase angle (\(\phi\)), but here it incorrectly states that current lags voltage. In reality, current leads voltage, thus this is not correct.
• Option 3: \( \omega L = \frac{1}{\omega C} \) means \(XL = XC\), yielding \(\phi = 0^\circ\) and voltage/current are in phase. This is correct.
• Option 4: When \(\phi = 0\), the impedance is purely resistive (\(Z=R\)). This correctly corresponds to option 3.

The incorrect statement is Option 2, as the roles of current and voltage were inaccurately described when \(XL < XC\).